A key assumption when using the multinomial distribution is that the observations are independent. In many practical situations, the observations could be correlated or clustered and the probabilities within each cluster might vary, which may lead to overdispersion. In this paper we discuss two well-known approaches to model overdispersed multinomial data, the Dirichlet-multinomial model and the finite-mixture model. The difference between these two models has been illustrated via simulation study. The forest pollen data is considered as a practical example of overdisperse multinomial data. The overdispersion parameter,φ, has been estimated using two classical estimators.